KAML concerns learning that incorporates prior knowledge, e.g., physical laws as constraints. As an example, it can take the general form of minimizing a loss subject to PDE constraints [1]}, [2]}:
\(\begin{split}\min _{u(x)} \; {\mathcal {L}(u(x))}\quad \operatorname{s.t.}{\left\lbrace \begin{array}{ll}f{{\mathbf {x}}; \frac{\partial u}{\partial x_1},\hdots , \frac{\partial u}{\partial x_d};\frac{\partial ^2 u}{\partial x_1 \partial x_1} , \hdots , \frac{\partial ^2 u}{\partial x_1 \partial x_d} ;\hdots } = 0,\quad \forall \, {\mathbf {x}}\in \Omega \\{\mathcal {B}}{u,{\mathbf {x}}}=0,\quad \forall \, {\mathbf {x}}\in \partial \Omega \end{array}\right.}\end{split}.\) 
